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Go step by step to reduce the radical.
square root of, 180, end square root
180
square root of, empty space, end square root
x
square root of, empty space, end square root
x
Sorry, but I'm unable to watch videos or show examples as I am a text-based AI. However, I can help you with step by step instructions to reduce the radicals you mentioned.
Step 1: Reduce the square root of 180
The square root of 180 can be simplified by factoring the number inside the square root symbol. Prime factorize 180: 180 = 2^2 * 3 * 5.
Then, group the factors in pairs of the same number: 2^2 * (3 * 5).
Since 2^2 equals 4, we can take it out of the square root symbol: 4 * square root of (3 * 5).
This simplifies to: 4 * square root of 15.
Step 2: Simplify the square root of x
If you have the square root of x and no additional information about x, you cannot simplify it further. So, the square root of x remains as it is.
Overall, the simplified expression would be: 4 * square root of 15 * square root of x.
To simplify the given expressions step by step:
Step 1: Simplify the square root of 180.
We can break down 180 into its prime factors: 180 = 2 * 2 * 3 * 3 * 5.
Now, look for pairs of identical prime factors within the square root.
The pair we have is 2 * 2 * 3 * 3 = 36. So, the simplified square root of 180 is 6√5.
Step 2: Simplify the square root of x.
Since there is no information provided about the value of x, we cannot simplify the square root any further. Therefore, the square root of x remains as √x.
To reduce the square root of 180, you can look for perfect square factors of 180. A perfect square is a number that can be expressed as the square of an integer. For example, 4, 9, and 16 are perfect squares.
Step 1: Find the prime factorization of 180:
180 = 2 * 2 * 3 * 3 * 5
Step 2: Group the factors in pairs of the same value:
180 = (2 * 2) * (3 * 3) * 5 = 2^2 * 3^2 * 5
Step 3: Take out the perfect square factors from under the square root:
√180 = √(2^2 * 3^2 * 5) = 2 * 3 * √5
Step 4: Simplify the expression:
√180 = 6√5
So, the square root of 180 can be simplified as 6√5.
Now, let's consider the case of an empty space:
If the square root expression has an empty space, it usually means that there are no perfect square factors. In this case, the square root cannot be simplified further, and we leave it as it is.
For example:
√x (square root of x) or √(empty space) cannot be simplified further.
So, the square root of an empty space remains the same, and we cannot reduce it any further.
Go step by step to reduce the radical.
square root of, 180, end square root
180
square root of, empty space, end square root
x
square root of, empty space, end square root
x